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DJ Wild

Introduction

DJ Wild is a poker-based game in which deuces and a joker are wild. After making an Ante and Blind bet the player has a simple raise or fold decision to make. Then his hand is compared to the dealer's — the higher hand wins.

I first saw the game at the 2014 Global Gaming Expo. Later, I saw it at the New York New York casino in Las Vegas on April 23, 2015. I've since heard of other placements. Here is all I know about as of April 27, 2015:

Las Vegas: New York New York

Michigan: Greektown casino

Ohio: Cleveland Horseshoe

California: Unknown

United Kingdom: Unknown

Rules

A 53-card deck is used, including a single joker.

Hands are ranked as follows, from highest to lowest:

Five wilds

Royal flush

Five of a kind

Straight flush

Four of a kind

Full house

Flush

Straight

Three of a kind

Two pair

Pair

Ace high or less

Play starts with the player making equal bets on the Ante and Blind. The player may also make an optional Trips side bet.

The dealer shall deal the player and himself five cards each. Dealer cards are dealt face down.

After examining his cards, the player may either fold or make a Play bet. The Play bet must be equal to two times the Ante.

The dealer shall reveal his cards and compare his hand to the player's, the higher poker value wins.

If the dealer has the higher hand, then the player shall lose the Ante, Blind, and Play bets.

If the two hands tie, then the Ante, Blind, and Play bets shall push.

If the player has the higher hand, then the Ante and Play bets shall pay even money. The Blind bet will pay according to the pay table below. All wins shown are on a "to one" basis.

The Trips bet shall pay according to the poker value of the player's bet only. More information is available on the Trips bet at the bottom of this page.

Blind Bet Pay Table

Player Hand

Pays

Five Wilds

1000

Royal Flush

50

Five of a Kind

10

Straight Flush

9

Four of a Kind

4

Full House

3

Flush

2

Straight

1

Three of a Kind or Less

Push

Analysis

The following table shows the number of combinations, probability, and contribution to the return of all possible events.

DJ Wild — Analysis

Event

Pays

Combinations

Probability

Return

Player wins with five wilds

1003

1,712,304

0.00000035

0.00034952

Player wins with royal flush

53

1,719,017,200

0.00034984

0.01854133

Player wins with five of a kind

13

2,396,963,100

0.00048781

0.00634147

Player wins with straight flush

12

6,243,236,040

0.00127056

0.01524670

Player wins with four of a kind

7

88,035,952,768

0.01791616

0.12541313

Player wins with full house

6

25,233,599,448

0.00513528

0.03081168

Player wins with flush

5

31,727,826,728

0.00645692

0.03228459

Player wins with straight

4

138,585,030,624

0.02820338

0.11281354

Player wins with three of a kind or less

3

1,944,630,013,152

0.39575088

1.18725263

Tie

0

560,641,504

0.00011410

0.00000000

Player folds

-2

1,507,375,457,280

0.30676538

-0.61353075

Dealer wins

-4

1,167,263,654,092

0.23754936

-0.95019744

Total

4,913,773,104,240

1.00000000

-0.03467361

The lower right cell shows an expected loss of 3.47% of a unit. This means if the player bets one unit each on the Ante and Blind, then he can expect to lose 3.47% of one of them. For example, if the player starts with bets of $10 on both the Ante and Blind, then he can expect to lose $10 &times 3.47% = 35¢ on average per hand.

The house edge is 3.47% relative to just the Ante bet, or 1.73% relative to both initial required bets, the Ante and Blind.

However, I think an appropriate measure of how good of a value the game is is the Element of Risk. This is the ratio of the expected loss to the total amount bet. On average, the player will raise 69.32% of the time, for an average bet of 2 + 69.32×2 = 3.39 units. The Element of Risk is thus 3.47%/3.39 = 1.02%.

If you're wondering where the house advantage lays, it is in the Blind bet. That wins 5.98% of the time only and carries an expected player loss of 38.2%.

Strategy

The strategy to DJ Wild is conveniently quite simple, as follows:

Raise with a pair of fours or better, except with two fours and a three singleton. Otherwise fold.

The three singleton exception makes sense because a pair of fours will beat a pair of threes, and the chances of the dealer getting a pair of threes is significantly less with one of them in the player's hand.

Player collusion would likely be powerful in this game. If you and the other players don't have any wild cards, then I would be more inclined to fold with a marginal hand, because of the increased probability the dealer will get one or more wild cards. Likewise, with a lot of wilds out, the player should be more inclined to raise. I'll leave it to Grosjean, Jacobson, and How to figure out the details on that.

Trips

As mentioned in the rules, Trips is an optional side bet that pays based only on the value of the player's hand. The player must have at least a three of a kind to win. Wins pay more if they are natural, as opposed to using a wild card. If a hand has a deuce, but still counts it as a deuce (for example an A2345 straight), then it shall pay as a natural win.

There are four pay tables available. The following table shows the probability and return of all possible outcomes under the Trip pay table used at the New York New York.

Trips Bet — "90-30-6" New York New York Pay Table

Player Hand

Wild/Natural

Pays

Combinations

Probability

Return

Royal flush

Natural

1,000

4

0.000001

0.001394

Straight flush

Natural

200

36

0.000013

0.002509

Four of a kind

Natural

90

528

0.000184

0.016559

Full house

Natural

40

3,168

0.001104

0.044158

Flush

Natural

30

5,108

0.001780

0.053400

Straight

Natural

20

10,200

0.003554

0.071088

Three of a kind

Natural

6

42,240

0.014719

0.088316

Five wilds

Wild

2,000

1

0.000000

0.000697

Royal flush

Wild

100

1,000

0.000348

0.034847

Five of a kind

Wild

100

1,400

0.000488

0.048786

Straight flush

Wild

30

3,612

0.001259

0.037760

Four of a kind

Wild

6

51,160

0.017828

0.106966

Full house

Wild

5

11,880

0.004140

0.020699

Flush

Wild

4

13,848

0.004826

0.019302

Straight

Wild

3

73,800

0.025717

0.077151

Three of a kind

Wild

1

415,800

0.144894

0.144894

Loser

Either

-1

2,235,900

0.779145

-0.779145

Total

2,869,685

1.000000

-0.010617

The following table shows all three pay tables. The column headings show what each pays for a natural four of a kind, flush, and three of a kind. The bottom row shows the house advantage.

Trips Bet — All Pay Tables

Player Hand

Wild/Natural

90-25-7

90-30-6

90-25-6

60-25-6

Royal flush

Natural

1,000

1,000

1,000

1,000

Straight flush

Natural

200

200

200

200

Four of a kind

Natural

90

90

90

60

Full house

Natural

40

40

30

30

Flush

Natural

25

30

25

25

Straight

Natural

20

20

20

20

Three of a kind

Natural

7

6

6

6

Five wilds

Wild

2,000

2,000

2,000

2,000

Royal flush

Wild

100

100

100

90

Five of a kind

Wild

100

100

100

70

Straight flush

Wild

30

30

30

25

Four of a kind

Wild

6

6

6

6

Full house

Wild

5

5

5

5

Flush

Wild

4

4

4

4

Straight

Wild

3

3

3

3

Three of a kind

Wild

1

1

1

1

Loser

Either

-1

-1

-1

-1

House edge

0.48%

1.06%

3.06%

6.05%

Acknowledgement

I would like to thank Shufflemaster, the game owner, for providing me their math report, compiled by Elliot Frome. The analysis above is my own and agrees closely with the simulation in Elliot's report. Elliot deserves proper credit for being the first to think of the strategy indicated above.